DACs are now widely used for performing audio data conversion from digital form into analog form. Many DACs utilize sigma-delta modulators for performing transformation of higher-resolution digital signals into lower-resolution digital signals before they feed to DACs so as to improve the quality of an audio signal. The sigma-delta modulators use error feedback loops, where the difference between the two signals is measured and used to improve the signal conversion. The low-resolution signal typically changes more quickly than the high-resolution signal, and it can be filtered to recover the high-resolution signal with little or no loss of fidelity.
In general, the DAC converts a digital number (e.g., an 8-bit digital number) representing some analog value (e.g., a specific volume magnitude) into that analog value by generating a particular voltage. Such conversions are typically not completely accurate, and imperfect matching (also known as mismatches) of levels may result in an imperfect transfer function of digital signals into analog signals. Mismatched analog components in the DACs may cause integral nonlinearity errors, which in turn may give rise to harmonic distortion and poor signal-to-noise ratio (SNR). If a particular application requires an output audio signal greater than 17-bit (i.e., SNR>105 dB), the analog components generally need to match to 17-bit accuracy. However, analog components typically cannot match to 17-bit accuracy due to variability amongst the elements (transistors, switches, capacitors, and so forth) that comprise the DACs and sigma-delta modulators. Even after using advanced layout techniques, the matching generally is at best approximately 10-11 dB, yielding a SNR of approximately 70 dB, which results in poor performance in many audio applications. In most commercial applications, a SNR of over 100 dB may be needed.
Various techniques have been proposed to attempt to minimize such noise under at least some operating conditions. One such techniques refers to a dynamic element matching (DEM) scheme, which is used to convert signal nonlinearity (i.e., mismatch errors) into spectrally shaped noise and may greatly improve the SNR. A DEM scheme typically uses a scrambler to dynamically select a group of elements for each digital input code such that over time, each element is equally used. Conventional DEM schemes utilize single-pointer scrambling, which causes a discontinuity when the data switches from positive to negative and vice versa. The switching discontinuity may result in an ineffective averaging of the mismatch error, and hence poor SNR.